求三角函数二倍角公式 求高中数学三角函数公式，二倍角公式
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sin
cos
tan
cot
sec
csc
\u6b63\u5f26\u51fd\u6570
sin\uff08A\uff09=a/h
\u4f59\u5f26\u51fd\u6570
cos\uff08A\uff09=b/h
\u6b63\u5207\u51fd\u6570
tan\uff08A\uff09=a/b
\u4f59\u5207\u51fd\u6570
cot\uff08A\uff09=b/a
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\u4e24\u89d2\u548c\u516c\u5f0f sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB tan(A+B)=(tanA+tanB)/(1-tanAtanB) tan(A-B)=(tanA-tanB)/(1+tanAtanB) cot(A+B)=(cotAcotB-1)/(cotB+cotA) cot(A-B)=(cotAcotB+1)/(cotB-cotA) \u500d\u89d2\u516c\u5f0f tan2A=2tanA/[1-(tanA)^2] cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2 sin2A=2sinA*cosA \u4e09\u500d\u89d2\u516c\u5f0f sin3a=3sina-4(sina)^3 cos3a=4(cosa)^3-3cosa tan3a=tana*tan(\u03c0/3+a)*tan(\u03c0/3-a) \u534a\u89d2\u516c\u5f0f sin(A/2)=\u221a((1-cosA)/2) sin(A/2)=-\u221a((1-cosA)/2) cos(A/2)=\u221a((1+cosA)/2) cos(A/2)=-\u221a((1+cosA)/2) tan(A/2)=\u221a((1-cosA)/((1+cosA)) tan(A/2)=-\u221a((1-cosA)/((1+cosA)) cot(A/2)=\u221a((1+cosA)/((1-cosA)) cot(A/2)=-\u221a((1+cosA)/((1-cosA)) tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA) \u548c\u5dee\u5316\u79ef sin(a)+sin(b)=2sin((a+b)/2)cos((a-b)/2) sin(a)?sin(b)=2cos((a+b)/2)sin((a-b)/2) cos(a)+cos(b)=2cos((a+b)/2)cos((a-b)/2) cos(a)-cos(b)=-2sin((a+b)/2)sin((a-b)/2) tanA+tanB=sin(A+B)/cosAcosB \u79ef\u5316\u548c\u5dee\u516c\u5f0f sin(a)sin(b)=-1/2*[cos(a+b)-cos(a-b)] cos(a)cos(b)=1/2*[cos(a+b)+cos(a-b)] sin(a)cos(b)=1/2*[sin(a+b)+sin(a-b)] \u8bf1\u5bfc\u516c\u5f0f sin(-a)=-sin(a) cos(-a)=cos(a) sin(pi/2-a)=cos(a) cos(pi/2-a)=sin(a) sin(pi/2+a)=cos(a) cos(pi/2+a)=-sin(a) sin(pi-a)=sin(a) cos(pi-a)=-cos(a) sin(pi+a)=-sin(a) cos(pi+a)=-cos(a) tgA=tanA=sinA/cosA \u4e07\u80fd\u516c\u5f0f sin(a)= (2tan(a/2))/(1+tan^2(a/2)) cos(a)= (1-tan^2(a/2))/(1+tan^2(a/2)) tan(a)= (2tan(a/2))/(1-tan^2(a/2)) \u5176\u5b83\u516c\u5f0f a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c) [\u5176\u4e2d\uff0ctan(c)=b/a] a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c) [\u5176\u4e2d\uff0ctan(c)=a/b] 1+sin(a)=(sin(a/2)+cos(a/2))^2 1-sin(a)=(sin(a/2)-cos(a/2))^2 \u5176\u4ed6\u975e\u91cd\u70b9\u4e09\u89d2\u51fd\u6570 csc(a)=1/sin(a) sec(a)=1/cos(a) \u53cc\u66f2\u51fd\u6570 sinh(a)=(e^a-e^(-a))/2 cosh(a)=(e^a+e^(-a))/2 tgh(a)=sinh(a)/cosh(a) \u516c\u5f0f\u4e00\uff1a \u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u7ec8\u8fb9\u76f8\u540c\u7684\u89d2\u7684\u540c\u4e00\u4e09\u89d2\u51fd\u6570\u7684\u503c\u76f8\u7b49\uff1a sin\uff082k\u03c0\uff0b\u03b1\uff09\uff1dsin\u03b1 cos\uff082k\u03c0\uff0b\u03b1\uff09\uff1dcos\u03b1 tan\uff082k\u03c0\uff0b\u03b1\uff09\uff1dtan\u03b1 cot\uff082k\u03c0\uff0b\u03b1\uff09\uff1dcot\u03b1 \u516c\u5f0f\u4e8c\uff1a \u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u03c0+\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a sin\uff08\u03c0\uff0b\u03b1\uff09\uff1d\uff0dsin\u03b1 cos\uff08\u03c0\uff0b\u03b1\uff09\uff1d\uff0dcos\u03b1 tan\uff08\u03c0\uff0b\u03b1\uff09\uff1dtan\u03b1 cot\uff08\u03c0\uff0b\u03b1\uff09\uff1dcot\u03b1 \u516c\u5f0f\u4e09\uff1a \u4efb\u610f\u89d2\u03b1\u4e0e -\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a sin\uff08\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1 cos\uff08\uff0d\u03b1\uff09\uff1dcos\u03b1 tan\uff08\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1 cot\uff08\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1 \u516c\u5f0f\u56db\uff1a \u5229\u7528\u516c\u5f0f\u4e8c\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u5230\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a sin\uff08\u03c0\uff0d\u03b1\uff09\uff1dsin\u03b1 cos\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcos\u03b1 tan\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1 cot\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1 \u516c\u5f0f\u4e94\uff1a \u5229\u7528\u516c\u5f0f\u4e00\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u52302\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a sin\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1 cos\uff082\u03c0\uff0d\u03b1\uff09\uff1dcos\u03b1 tan\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1 cot\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1 \u516c\u5f0f\u516d\uff1a \u03c0/2\u00b1\u03b1\u53ca3\u03c0/2\u00b1\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a sin\uff08\u03c0/2\uff0b\u03b1\uff09\uff1dcos\u03b1 cos\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dsin\u03b1 tan\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcot\u03b1 cot\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dtan\u03b1 sin\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dcos\u03b1 cos\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dsin\u03b1 tan\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dcot\u03b1 cot\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dtan\u03b1 sin\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcos\u03b1 cos\uff083\u03c0/2\uff0b\u03b1\uff09\uff1dsin\u03b1 tan\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcot\u03b1 cot\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dtan\u03b1 sin\uff083\u03c0/2\uff0d\u03b1\uff09\uff1d\uff0dcos\u03b1 cos\uff083\u03c0/2\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1 tan\uff083\u03c0/2\uff0d\u03b1\uff09\uff1dcot\u03b1 cot\uff083\u03c0/2\uff0d\u03b1\uff09\uff1dtan\u03b1 (\u4ee5\u4e0ak\u2208Z)
二倍角公式
sin2α=2sinαcosα
tan2α=2tanα/(1-tan^2(α))
cos2α=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)
扩展资料：
半角公式
sin^2(α/2)=(1-cosα)/2
cos^2(α/2)=(1+cosα)/2
tan^2(α/2)=(1-cosα)/(1+cosα)
tan(α/2)=sinα/(1+cosα)=(1-cosα)/sinα
同角三角函数的基本关系式
倒数关系：tanα ·cotα=1、sinα ·cscα=1、cosα ·secα=1；
商的关系： sinα/cosα=tanα=secα/cscα、cosα/sinα=cotα=cscα/secα；
和的关系：sin2α+cos2α=1、1+tan2α=sec2α、1+cot2α=csc2α；
平方关系：sin²α+cos²α=1。
二倍角公式 sin2a=2sinacosa
cos2a=cos^2(a)-sin^2(a)=2cos^2(a)-1=1-2sin^2(a)
tan2a=2tana/[1-tan^2(a)]
二倍角公式 sin2a=2sinacosa
cos2a=cos^2(a)-sin^2(a)=2cos^2(a)-1=1-2sin^2(a)
tan2a=2tana/[1-tan^2(a)]
20190723 数学02
绛旓細浜屽嶈鍏紡 sin2伪=2sin伪cos伪 tan2伪=2tan伪/(1-tan^2(伪))cos2伪=cos^2(伪)-sin^2(伪)=2cos^2(伪)-1=1-2sin^2(伪)
绛旓細浜屽嶈鍏紡锛sin2伪=2sin伪cos伪 tan2伪=2tan伪/(1-tan^2(伪))cos2伪=cos^2(伪)-sin^2(伪)=2cos^2(伪)-1=1-2sin^2(伪)tan2伪=2tan伪/锛1-tan^2伪锛
绛旓細涓夎鍑芥暟鐨勪簩鍊嶈鍏紡鏄敤鏉ヨ绠楁煇涓涓鐨勪袱鍊嶈鐨勬寮︺佷綑寮︺佹鍒囧肩殑鍏紡銆傚叿浣撴潵璇达紝瀵逛簬浠绘剰瑙捨革紝鍏朵簩鍊嶈涓2胃锛岄偅涔堝叾姝ｅ鸡銆佷綑寮︺佹鍒囩殑浜屽嶈鍏紡鍒嗗埆濡備笅锛氭寮︾殑浜屽嶈鍏紡锛歴in(2胃) = 2sin胃cos胃 浣欏鸡鐨勪簩鍊嶈鍏紡锛歝os(2胃) = cos²胃 - sin²胃 姝ｅ垏鐨勪簩鍊嶈...
绛旓細涓夎鍑芥暟浜屽嶈鍏紡鏈夛細姝ｅ鸡浜屽嶈鍏紡sin2A=2sinAcosA銆佷綑寮︿簩鍊嶈鍏紡cos2a=锛坈osa锛塣2-锛坰ina锛塣2=2锛坈osa锛塣2-1=1-2锛坰ina锛塣2浠ュ強姝ｅ垏浜屽嶈鍏紡tan2A=2tanA/[1-锛坱anA锛塣2]銆備簩鍊嶈鍏紡鏄暟瀛︿笁瑙掑嚱鏁颁腑甯哥敤鐨勪竴缁勫叕寮忥紝閫氳繃瑙捨辩殑涓夎鍑芥暟鍊肩殑涓浜涘彉鎹㈠叧绯绘潵琛ㄧず鍏朵簩鍊嶈2伪鐨勪笁...
绛旓細1銆乻in2伪=2sin伪cos伪锛宼an2伪=2tan伪1tan^2伪锛宑os2伪=cos^2伪sin^2伪=2cos^2伪1=12sin^2伪浜屽嶈鍏紡鏄暟瀛︿笁瑙掑嚱鏁颁腑甯哥敤鐨勪竴缁勫叕寮锛岄氳繃瑙捨辩殑涓夎鍑芥暟鍊肩殑涓浜涘彉鎹㈠叧绯绘潵琛ㄧず銆2銆佷綑寮︿簩鍊嶈浣欏鸡浜屽嶈鍏紡鏈変笁缁勮〃绀哄舰寮忥紝涓夌粍褰㈠紡绛変环1cos2a=2cos2伪1 2cos2伪=12sin2伪 3...
绛旓細cos 鐨浜屽嶈鍏紡鏄細cos2伪=cos2伪-sin2伪=2cos2-1=1-2sin2伪銆傚湪涓夎鍑芥暟涓紝鎴戜滑缁忓父浼氶亣鍒伴渶瑕璁＄畻瑙鐨勫嶆暟瀵瑰簲鐨勪笁瑙掑嚱鏁板肩殑鎯呭喌銆傚叾涓紝cosine鍑芥暟鍦ㄨ绠楄鐨勫嶈鏃跺挨涓哄父瑙併傚嶈鏈甯歌鐨勬湁cos2胃銆乧os4胃鍜宑os胃/2锛屽畠浠湪瑙ｅ喅鍚勭涓夎闂涓捣鍒颁簡閲嶈鐨勪綔鐢ㄣ傝鎴戜滑鏉ヤ粙缁峜os2胃...
绛旓細浜屽嶈鍏紡 sin(2a)=2sin(a)cos(a)cos(2a)=cos^2(a)-sin^2(a)=2cos^2(a)-1=1-2sin^2(a)tan(2a)=2tan(a)/(1-tan^2(a))cot(2a)=(cot^2(a)-1)/2cot(a)
绛旓細涓夎鍑芥暟浜屽嶈鍏紡鏈夛細1銆乼an2A=2tanA/銆2銆乧os2a=锛坈osa锛夛季2-锛坰ina锛夛季2=2锛坈osa锛夛季2-1=1-2锛坰ina锛夛季2銆3銆乻in2A=2sinA*cosA銆傛槸鏁板涓夎鍑芥暟涓父鐢ㄧ殑涓缁勫叕寮忥紝閫氳繃瑙捨辩殑涓夎鍑芥暟鍊肩殑涓浜涘彉鎹㈠叧绯绘潵琛ㄧず鍏朵簩鍊嶈2伪鐨勪笁瑙掑嚱鏁板硷紝浜屽嶈鍏紡鍖呮嫭姝ｅ鸡浜屽嶈鍏紡銆佷綑寮︿簩鍊嶈鍏紡...
绛旓細鍊嶈鍏紡锛屾槸涓夎鍑芥暟涓潪甯稿疄鐢ㄧ殑涓绫诲叕寮忋傚氨鏄妸浜屽嶈鐨勪笁瑙掑嚱鏁扮敤鏈鐨勪笁瑙掑嚱鏁拌〃绀哄嚭鏉ャ傚湪璁＄畻涓彲浠ョ敤鏉ュ寲绠璁＄畻寮忋佸噺灏姹備笁瑙掑嚱鏁鐨勬鏁帮紝鍦ㄥ伐绋嬩腑涔熸湁骞挎硾鐨勮繍鐢ㄣ傚嶈鍏紡鏈夊摢浜 鍊嶈鍏紡锛歋in2A=2SinA.CosA Cos2A=CosA^2-SinA^2=1-2SinA^2=2CosA^2-1 tan2A=锛2tanA锛/锛1-tanA...
绛旓細浜屽嶈鍏紡锛氬崐瑙掑叕寮忥細
